The optical properties of TlGaSeS layered single crystals have been investigated by measuring the transmissions and the reflections in the wavelength region between 400 and 1100 nm. The optical indirect transitions with a band gap energy of 2.27 eV and direct transitions with a band gap energy of 2.58 eV were found by means of the analysis of the absorption data at the room temperature. The rate of change of the indirect band gap with temperature, that is, gamma = -3.2 x 10(-4) eV/K, was determined from the transmission measurements in the temperature range of 10 - 300 K. The absolute zero value of the band gap energy was obtained as E-gi(0) = 2.34 eV. The dispersion of the refractive index is discussed in terms of the Wemple-DiDomenico single-effective-oscillator model. The oscillator energy, the dispersion energy, the oscillator strength, and the zero-frequency refractive index, which are all refractive-index dispersion parameters, were found to be 4.71 eV, 28.98 eV, 8.88 x 10(13) m(-2) and 2.67, respectively. The parameters of the monoclinic unit cell were found by studying the X-ray powder diffraction.